Hi Jennifer: Your seedlings look healthy! Before looking at your photos, I was thinking it could be a fungi from the soil. But your soil looks like a sterile potting medium rather than garden dirt or topsoil mix so that's good.

To me it looks like the vermiculite or perlite in the soil mix has become stained from the tannins leaching from the organic matter. Often peat or decomposed wood is used to make the organic component of potting soil.  I think your plants are fine and keep doing what you've been doing. 

I wish you a bumper crop of tomatoes!